(722e) An Immersed Boundary Method for Rapid Dynamic Simulation of Electrokinetic Phenomena in Dispersions of Nanoparticles in Concentrated Electrolytes

Electrokinetic phenomena are ubiquitous in soft matter systems from stabilization of nanoparticle dispersions to transport of charged species in electric fields to self-assembly of responsive functional materials. Predictive theories and models are necessary to facilitate rational design and use of such systems. Modelling these non-equilibrium processes is notoriously difficult because it involves a complicated coupling between electrostatic interactions among ions and particles and their electrophoretic motion. This coupling can be captured directly in dynamic simulations with explicit ions, but there are numerous computational challenges. Computing the long-ranged, many-bodied hydrodynamic and electrostatic forces requires solving several systems of equations at each time step. Additionally, the simulation must cover multiple length and time scales to accurately resolve the motion of small ions and larger macromolecules and nanoparticles. Current simulation techniques either sacrifice key physics to accelerate the calculations or limit high fidelity models to very small length and time scales, neither of which allows for an accurate description of real electrokinetic processes.

Here, we present an accelerated immersed boundary method for dynamic simulations of dispersions of charged and polarizable nanoparticles in concentrated electrolyte solutions. The parallelized method scales nearly linearly with the number of ions and nanoparticles and is implemented on single graphics processing units (GPU), allowing us to reach size and time scales previously inaccessible to dynamic simulations. Ions are explicitly modelled, and the many-bodied electrostatic and hydrodynamic forces are correctly accounted for. The nanoparticles may be of arbitrary shape and charge, and polarization and fluctuations of the particle charge distribution are incorporated into the calculations. We use our method to directly investigate complicated nonlinear effects in soft matter electrokinetics, such as polarization of the double layer and nanoparticle during electrophoresis and the structure of interacting ion layers in the self-assembly of charged, polarizable colloids.